It is well-known that if $X$ and $Y$ are independent binomial random variables with parameters $(n_1,p)$ and $(n_2,p)$ respectively, $Z = X+Y$ has a binomial distribution with with parameters $(n_1+n_2,p)$.
I was wondering if $Y$ is binomial with parameters $(n_2, 1-p)$ what will be the distribution of $X+Y$?